Free access article

Issue M2AN Volume 37, Number 4, July-August 2003 Biological and Biomedical Applications Page(s) 557 - 580 DOI 10.1051/m2an:2003047

M2AN, Vol. 37, N°4, pp. 557-580
DOI: 10.1051/m2an:2003047

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke¹, Kim H. Parker², Ling Y. Wee³, Nicholas M. Fisk³ and Spencer J. Sherwin<sup>1

1</sup>  Biomedical Flow Group, Department of Aeronautics, Imperial College London, South Kensington Campus London SW7 2AZ, UK. v.shenton@imperial.ac.uk., s.sherwin@imperial.ac.uk., web page: http://www.ae.imperial.ac.uk/staff/sherwin
²  Department of Bioengineering, Imperial College London, South Kensington Campus London SW7 2AZ, UK.
³  Institute of Reproductive and Developmental Biology, Imperial College London at Queen Charlotte's Hospital, Hammersmith Campus.

Abstract
In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ hp element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance. We then present results for the waveform patterns and the volume fluxes throughout a simplified model of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. The effects of varying the time period of the two fetus' heart beats, increasing the input flux of one fetus and the role of terminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by the computational model and demonstrate the applicability of the methods to the simulation of flows in arterial networks.

Mathematics Subject Classification. 92C35, 76Z05.

Key words: Wave propagation, mathematical model, spectral/ hp element, arterial networks, monochorionic placentas, non-linear.


© EDP Sciences, SMAI 2003

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